Having relatively recently learned to play the game, I have a few things to add to this.

First, Shrike, you have a stray [ u ] in your post which caused most of the text to get underlined. Should probably fix that.

Second, you need to upgrade weapons regularly. In my first playthrough I stuck to particle weapons for a long time (about halfway through the Outer Realms!), because they were accurate, long-ranged, fast-firing, and didn't seem to be that much less powerful, according to the numbers, than the top-tier tech. The problems with that approach are twofold: first, because particle weapons don't have any WMD, I was more or less incapable of taking out capital ships (ask me about spending ten minutes plinking at a Phobos from extreme range! Go on!), and second, the game applies a hidden damage modifier based on the "level" of your damage type compared to the level of the armor it's firing against. The particle damage type is level-3 (after laser and kinetic, before blast), which means that it was facing a steep damage penalty against enemies with level-6+ armor.

My go-to upgrades these days are howitzers, which have good WMD and range, at the cost of slow firing rate and projectile speed. They're definitely not great for dealing with fighters, but they're reliable for taking down capships and bases. But feel free to experiment; the main thing is that you will have to transition away from particle weapons, and you should try to find something with a decent amount of WMD.

Third, try using launchers. They're not to everyones' tastes, but they can really speed up killing those big targets. NAMI ammo is ubiquitous in the early game, so there's really not that much of an investment in using a NAMI launcher. And unlike most earlygame weapons, they have decent WMD, making it a ton easier to take down Charon capships. Launchers fire simultaneously with your main weapon, effectively doubling your offense even before WMD is considered; this makes dangerous fights (including most of the arena) a lot safer. The faster the enemy dies, the less time they have to hurt you with, after all. My default upgrade path is NAMI -> Makayev -> Ares, but other launchers are definitely worth experimenting with.

Fourth, try the mouse controls. Again, they're not to everyones' tastes, but I personally find it a lot easier to aim precisely by using the mouse than by using the keyboard. It's hard to use the keyboard to precisely select the exact aiming frame you want out of the 120 available to you, especially with a fast-turning ship. In particular, kiting and dealing with Slaver camps becomes a lot easier when you have precise aim; leading targets that are trying to circle around you also becomes easier.

Fifth, and this is mostly a quality of life thing, get a cargo hold. The easiest to find are usually miner's holds, at friendly mining stations, but Commonwealth stations may randomly stock the basic hold, and you can get smuggler's holds at Black Market stations (get a Black Market ID chip by delivering some illegal goods to a hotel). Most ships have a very tight cargo capacity if you don't get a hold, which makes looting and selling a tedious process; adding an extra 50 tons to that capacity can greatly improve the rate at which you bring in money, which in turn directly determines how powerful your ship is. Note that while the miner and standard hold have higher capacities than the smuggler's hold, each ship has a limit on how much their capacity can be expanded which mostly makes these differences moot. Selling illegal goods that you find (especially fusion triggers) can be quite lucrative.